Knight is best known as the author of the book Risk Uncertainty and Profit, (PDF) based on his Ph.D. dissertation at Cornell University. In that book, he carefully distinguished between economic risk and uncertainty. Situations with risk were those where the outcomes were unknown but governed by probability distributions known at the outset. He argued that these situations, where decision making rules such as maximising expected utility can be applied, differ in a deep way from "uncertain" ones, where the outcomes were likewise random, but governed by an unknown probability model. Knight argued that uncertainty gave rise to economic profits that perfect competition could not eliminate.

While most economists now acknowledge Knight's distinction between risk and uncertainty, the distinction has not resulted in much theoretical modelling or empirical work. (emphasis added)

Well, fancy that! Who could'a imagined? Perhaps one of the perks of being the guy who first described a field is the opportunity to systematically ignore the implications when those implications were awkward. I can hear his ghost responding to an accusation that his life's work paved the road to the biggest financial calamity since the Great Depression whilst ignoring Knightian uncertainty: "Don't harangue me about risk! I wrote the book."

This seems to be the focus of Raphaële Chappe's academic work and one her background well equips her to investigate with authority.

Along with Wynne Godley and Steve Keen, of course, with reference to empirical work and modeling. But that was the summary of the author of the wiki article, which was addressing the field of economics generally.

In the cited article Raphaële Chappe notes:

J.M. Keynes was perhaps the first economist to grasp the full significance of radical uncertainty for economic analysis. Author of A Treatise on Probability published in 1921, Keynes developed the view that it is not always possible to assign a numerical value to probabilities -- a point unrelated to the practicality of measurement (Keynes, 1921). The frequentist approach breaks down in some situations. It is impossible to find strictly relevant frequency ratios because even if a relevant statistical database were to exist, the presence of additional information might make the database inadequate for the computation of a numerical probability.

In his Treatise, Keynes gave the example of the outcome of a Presidential election, or something as ordinary as the probability that we reach home alive if we are out for a walk. In a famous later article, he gave the example of "the price of copper and the rate of interest twenty years hence" (Keynes, 1937). The implication for Keynes' General Theory was that macroeconomic variables such as investment and consumption are shaped by many factors which are not susceptible to probabilistic analysis (fundamentally different from the outcomes of a game of roulette).

Events determined by human decisions (much of which, he argued, are driven by `animal spirits' - ideas and attitudes determined by intangible psychological motivations) do not lend themselves to the calculation of probabilities. We can think of many events that are likely to influence economic variables (such as prices and incomes) and economic decisions (such as the level of investment) but are by their very nature radically uncertain, such as the occurrence of wars, changes of government, inventions, climatic changes.

Yet this insight was completely neglected in the mainstream economics that followed (and arguably marginalized by Keynes's own mainstream interpreters, such as J.R. Hicks). The notion of calculable risk has permeated modern microeconomics, starting with its formalization in the concept of `expected utility theory' introduced by J. von Neumann and O. Morgenstern in 1947. There has been a triumph of risk over uncertainty (Reddy, 1996). It is something of an irony of history that the importance of the incalculability of risk was first explored in a discipline which has since failed to take the insight into account. This irony is not lost to other social scientists:

"The discovery of the incalculability of risk is closely connected to the discovery of the importance of not-knowing to risk calculation, and it is part of another kind of irony, that surprisingly this discovery of not-knowing occurred in a scholarly discipline which today no longer wants to have anything to do with [it]: economics." (Beck, 2006: 334).

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."

J.M. Keynes was perhaps the first economist to grasp the full significance of radical uncertainty for economic analysis. Author of A Treatise on Probability published in 1921, Keynes developed the view that it is not always possible to assign a numerical value to probabilities -- a point unrelated to the practicality of measurement (Keynes, 1921). The frequentist approach breaks down in some situations. It is impossible to find strictly relevant frequency ratios because even if a relevant statistical database were to exist, the presence of additional information might make the database inadequate for the computation of a numerical probability.

In his Treatise, Keynes gave the example of the outcome of a Presidential election, or something as ordinary as the probability that we reach home alive if we are out for a walk. In a famous later article, he gave the example of "the price of copper and the rate of interest twenty years hence" (Keynes, 1937). The implication for Keynes' General Theory was that macroeconomic variables such as investment and consumption are shaped by many factors which are not susceptible to probabilistic analysis (fundamentally different from the outcomes of a game of roulette).

To Keynes, probability is a branch of logic: the theory of rational thought under uncertainty. Ordinary logic is just the subset of rational thought dealing with certain (or certainly false) propositions. I think this is a really interesting approach. Probability to Keynes is relative but not subjective. That is, probability is always relative to some data (or hypotheses), and so it is in a way subjective since each of us has different data/knowledge/experience, even different mental acuity. However, Keynes' probability is not subjective in the sense that a correctly formed probabilistic reasoning, being enunciated relative to explicit hypotheses, should be valid independently. Keynes writes at length about the problem of induction (reasoning from particular, though possibly numerous, observations to general statements) and he stresses that, contrary to what has been asserted by philosophers in the past, the fact that an inductive conclusion turns out to be false does not invalidate the inductive reasoning relative to the information available at the time the conclusion was formulated.

Reading Keynes' ideas on probability, it is absolutely not surprising that he takes the position he does on the role of uncertainty and expectations in The General Theory. Also it helps to understand how all the "deviations from rationality" that neoclassicals like to talk about can actually be rational behaviour under uncertainty form a Keynesian point of view.

We might also say of Knight that his decision, after having written the book Risk Uncertainty and Profit, to ignore the part about uncertainty was, from a certain point of view, rational. After all, if he emphasizes uncertainty he blows up the utility of his work for the generation of profits. And Knight had to know from whence came the donations that funded private universities and what were the interests of those donors.

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."

One end of the spectrum of uncertainty is events which have a well defined spectrum of possible outcomes and well defined underlying probability distributions, but where it is excessively costly, time-consuming or otherwise onerous to establish the distribution ahead of making a decision. At the other end of the spectrum of uncertainty you have the Outside Context Event.

Somewhere around the middle you have the sort of event where the span of possible outcomes is not sufficiently well defined that it can be described by a probability distribution, but which is none the less sufficiently predictable that it is possible to devise heuristics and contingency plans.

Those are all "uncertainty," but they are very different sorts of uncertainty. (Indeed it is risk, not uncertainty, that is the extreme edge case of the human condition.)

- Jake

If you only spend 20 minutes of the rest of your life on economics, go spend them here.

I thought it still exists. One of the strangest things for me when visiting Israel is hearing regular AIG commercials on the radio. (There are plenty of other strange things on the radio, but I'm used to them....)

Owing to the convexity of the payoff of out-of-the money options, an extremely small probability of a large deviation unseen in past data justifies rationally buying them, or at least justifies excessive caution in not being exposed to them, particularly those options that are extremely nonlinear in response to market movement or changes in implied volatility. One needs, for instance, a minimum of 2000 years of stock market data to assert that some tail options are "expensive". The paper presents errors in Ilmanen (2012), which provides an exhaustive list of all arguments in favor of selling insurance on small probability events. The paper goes beyond Ilmanen (2012) and suggests an approach to analyze the payoff and risks of options based on the nonlinearities in the tails.